Functional Programming

Monday, May 22

Today we will…

  • Project Proposal + Data
  • New Material1
    • Review vectorization
    • The map() family
  • PA 8: The 12 Days of Christmas Starter Functions

Project Proposal + Data

You must complete the objectives and write up the written components outlined under Section 1 on the Project Details page on Canvas.

  • Due on Canvas on Monday, 5/29.

Performing Repeated Tasks

Repetition

Type out the task over and over.

https://bookdown.org/hneth/ds4psyl

Do not do this.

Iteration

Repeatedly execute the same operation over and over.

  • Loops (e.g., for() and while()) allow us to iterate.
for(i in 1:10){
  print(i^2)
}
[1] 1
[1] 4
[1] 9
[1] 16
[1] 25
[1] 36
[1] 49
[1] 64
[1] 81
[1] 100

https://bookdown.org/hneth/ds4psyl

Vectorization

Many operations in R are vectorized.

  • These functions operate on vectors of values rather than a single value.
  • We can iterate without writing a loop.
x <- seq(from = -4, to = 6)
x
 [1] -4 -3 -2 -1  0  1  2  3  4  5  6

Loop:

for(i in 1:length(x)){
  x[i] <- abs(x[i])
}
x
 [1] 4 3 2 1 0 1 2 3 4 5 6

Vectorized:

abs(x)
 [1] 4 3 2 1 0 1 2 3 4 5 6

Vectorization

Not every function is (or can be) vectorized.

  • E.g., a function using if() statements cannot operate on vectors.
pos_neg_zero <- function(x){
  if(x > 0){
    return("Greater than 0!")
  } else if (x < 0){
    return("Less than 0!")
  } else {
    return("Equal to 0!")
  }
}

x <- seq(from = -4, to = 4)
pos_neg_zero(x)
Error in if (x > 0) {: the condition has length > 1

The error us that if(x > 0) can only be checked for something of length 1 (a single number, not a vector).

Vectorization

Not every function is (or can be) vectorized.

  • E.g., a function using if() statements cannot operate on vectors.
pos_neg_zero <- function(x){
  if(x > 0){
    return("Greater than 0!")
  } else if (x < 0){
    return("Less than 0!")
  } else {
    return("Equal to 0!")
  }
}

x <- seq(from = -4, to = 3)
pos_neg_zero(x)
Error in if (x > 0) {: the condition has length > 1
result <- rep(NA, length(x))
for(i in 1:length(x)){
  result[i] <- pos_neg_zero(x[i])
}

result
[1] "Less than 0!"    "Less than 0!"    "Less than 0!"    "Less than 0!"   
[5] "Equal to 0!"     "Greater than 0!" "Greater than 0!" "Greater than 0!"

Vectorization

Not every function is (or can be) vectorized.

  • E.g., a function using if() statements cannot operate on vectors.
  • A vectorized version of if() statements? case_when()
pos_neg_zero <- function(x){
  state <- case_when(x > 0 ~ "Greater than 0!", 
                     x < 0 ~ "Less than 0!", 
                     .default = "Equal to 0!")
  return(state)
}

x <- seq(from = -4, to = 3)
pos_neg_zero(x)
[1] "Less than 0!"    "Less than 0!"    "Less than 0!"    "Less than 0!"   
[5] "Equal to 0!"     "Greater than 0!" "Greater than 0!" "Greater than 0!"

Some functions cannot be vectorized!

Applying class() to a single variable in a datqaframe returns the data type of that column:

class(penguins[[1]])
[1] "factor"

Trying to apply class() to every variable in a dataframe returns the data type of the dataframe:

class(penguins)
[1] "tbl_df"     "tbl"        "data.frame"

What can we do instead?

Write a for() loop…

data_type <- rep(NA, length = ncol(penguins))
for(i in 1:ncol(penguins)){
  data_type[i] <- class(penguins[[i]])
}

# format table nicely
tibble(column = names(penguins), 
       type = data_type) |> 
  pivot_wider(names_from = column, 
              values_from = type) |>  
  knitr::kable() |>
  kableExtra::kable_styling(font_size = 30)
species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex year
factor factor numeric numeric integer integer factor integer

… but loops are computationally intensive!

What can we do instead?

What about across()?

  • Easily perform the same operation on multiple columns.
penguins |> 
  summarise(across(.cols = everything(), 
                   .fns = class))
# A tibble: 1 × 8
  species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
  <chr>   <chr>  <chr>          <chr>         <chr>             <chr>      
1 factor  factor numeric        numeric       integer           integer    
# ℹ 2 more variables: sex <chr>, year <chr>

Ugh. Internally, across() uses a for() loop!

for (j in seq_fns) {
  fn <- fns[[j]]
  out[[k]] <- fn(col, ...)
  k <- k + 1L

What can we do instead?


Functional Programming

To understand computations in R, two slogans are helpful:

  • Everything that exists is an object.

  • Everything that happens is a function call.

John Chambers (creator of the pre-cursor to R)

Functional Programming

What’s the big picture?

  • We will use functions as the arguments to other functions!


Note

There are a slew of apply() functions you will likely come across.

We will instead focus on the purrr package and the map() family of functions.

purrr

The purrr package breaks common list manipulations into small, independent pieces.

This strategy involves two steps:

  1. Break a complex problem into smaller sub-problems.
    • We then compose the small pieces together with |>.
  2. Solve each sub-problem for a single element of a list.
    • Once done, purrr will generalize the solution to every element in the list.

Brief Review: Lists

A list is a 1-dimensional, heterogeneous data structure.

  • There are no restrictions on what data type or structure it can contain – values, vectors, other lists, dataframes, etc.
  • Lists are indexed with [] or [[]].
[[1]]
[1]  TRUE FALSE  TRUE  TRUE

[[2]]
     [,1] [,2]
[1,] 6.70  4.4
[2,] 5.58  6.0

[[3]]
[1] "A"
my_list[1]
[[1]]
[1]  TRUE FALSE  TRUE  TRUE
my_list[[2]]
     [,1] [,2]
[1,] 6.70  4.4
[2,] 5.58  6.0
my_list[[2]][1,2]
[1] 4.4

Brief Review: Lists

A dataframe / tibble is a specially formatted list of columns!

small_penguins <- penguins[1:8,]
small_penguins[3]
# A tibble: 8 × 1
  bill_length_mm
           <dbl>
1           39.1
2           39.5
3           40.3
4           NA  
5           36.7
6           39.3
7           38.9
8           39.2
small_penguins[[3]]
[1] 39.1 39.5 40.3   NA 36.7 39.3 38.9 39.2

The purrr package works for lists, so it works for dataframes.

map()

The map() function iterates through each item in a list and applies a function, then returns the new list.

Note: the first argument in map() is the list, so if we pipe into it, we only specify the function!

map() + Dataframes

A dataframe is just a list of columns – map() will apply a function to every column.

penguins |> 
  select(bill_length_mm:body_mass_g) |>
  map(~ mean(.x, na.rm = TRUE))
$bill_length_mm
[1] 43.92193

$bill_depth_mm
[1] 17.15117

$flipper_length_mm
[1] 200.9152

$body_mass_g
[1] 4201.754

Use a lambda function (with ~ and .x), just like in across()!

The map() Family

The map_xxx() variants allow you to specify the type of output you want.

  • map() creates a list.
  • map_chr() creates a character vector.
  • map_lgl() creates an logical vector.
  • map_int() creates a integer vector.
  • map_dbl() creates a numeric vector.

All take in a list and a function as arguments.

map() + penguins

Calculate the mean of each column.

penguins |> 
  select(bill_length_mm:body_mass_g) |> 
  map_dbl(~ mean(.x, na.rm = TRUE))
   bill_length_mm     bill_depth_mm flipper_length_mm       body_mass_g 
         43.92193          17.15117         200.91520        4201.75439 

Output is a vector of doubles.

Calculate the number of NAs in each column.

penguins |> 
  map_int(~ sum(is.na(.x)))
          species            island    bill_length_mm     bill_depth_mm 
                0                 0                 2                 2 
flipper_length_mm       body_mass_g               sex              year 
                2                 2                11                 0 

Output is a vector of integers.

Calculate the number of NAs in each column.

penguins |> 
  map_lgl(~ sum(is.na(.x)))
Error in `map_lgl()`:
ℹ In index: 3.
ℹ With name: bill_length_mm.
Caused by error:
! Can't coerce from an integer to a logical vector.

R returns an error if the output is of the wrong type!

  • Output is a logical vector??

map_if()

The map_if() function allows us to conditionally apply a function to each item in a list.

penguins |> 
  mutate(across(.cols = where(is.numeric), 
                .fns = scale))
# A tibble: 8 × 5
  species island    bill_length_mm[,1] bill_depth_mm[,1] sex   
  <fct>   <fct>                  <dbl>             <dbl> <fct> 
1 Adelie  Torgersen             -0.883             0.784 male  
2 Adelie  Torgersen             -0.810             0.126 female
3 Adelie  Torgersen             -0.663             0.430 female
4 Adelie  Torgersen             NA                NA     <NA>  
5 Adelie  Torgersen             -1.32              1.09  female
6 Adelie  Torgersen             -0.847             1.75  male  
7 Adelie  Torgersen             -0.920             0.329 female
8 Adelie  Torgersen             -0.865             1.24  male  
penguins |> 
  map_if(is.numeric, scale)
$species
  [1] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
  [8] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [15] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [22] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [29] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [36] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [43] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [50] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [57] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [64] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [71] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [78] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [85] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [92] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
 [99] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
[106] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
[113] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
[120] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
[127] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
[134] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
[141] Adelie    Adelie    Adelie    Adelie    Adelie    Adelie    Adelie   
[148] Adelie    Adelie    Adelie    Adelie    Adelie    Gentoo    Gentoo   
[155] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[162] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[169] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[176] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[183] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[190] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[197] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[204] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[211] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[218] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[225] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[232] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[239] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[246] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[253] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[260] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[267] Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo    Gentoo   
[274] Gentoo    Gentoo    Gentoo    Chinstrap Chinstrap Chinstrap Chinstrap
[281] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[288] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[295] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[302] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[309] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[316] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[323] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[330] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[337] Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap Chinstrap
[344] Chinstrap
Levels: Adelie Chinstrap Gentoo

$island
  [1] Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen
  [8] Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen
 [15] Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen Biscoe   
 [22] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
 [29] Biscoe    Biscoe    Dream     Dream     Dream     Dream     Dream    
 [36] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
 [43] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
 [50] Dream     Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
 [57] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
 [64] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Torgersen Torgersen
 [71] Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen
 [78] Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen
 [85] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
 [92] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
 [99] Dream     Dream     Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[106] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[113] Biscoe    Biscoe    Biscoe    Biscoe    Torgersen Torgersen Torgersen
[120] Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen
[127] Torgersen Torgersen Torgersen Torgersen Torgersen Torgersen Dream    
[134] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[141] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[148] Dream     Dream     Dream     Dream     Dream     Biscoe    Biscoe   
[155] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[162] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[169] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[176] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[183] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[190] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[197] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[204] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[211] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[218] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[225] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[232] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[239] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[246] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[253] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[260] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[267] Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe    Biscoe   
[274] Biscoe    Biscoe    Biscoe    Dream     Dream     Dream     Dream    
[281] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[288] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[295] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[302] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[309] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[316] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[323] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[330] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[337] Dream     Dream     Dream     Dream     Dream     Dream     Dream    
[344] Dream    
Levels: Biscoe Dream Torgersen

$bill_length_mm
              [,1]
  [1,] -0.88320467
  [2,] -0.80993901
  [3,] -0.66340769
  [4,]          NA
  [5,] -1.32279862
  [6,] -0.84657184
  [7,] -0.91983750
  [8,] -0.86488825
  [9,] -1.79902541
 [10,] -0.35202864
 [11,] -1.12131806
 [12,] -1.12131806
 [13,] -0.51687637
 [14,] -0.97478674
 [15,] -1.70744334
 [16,] -1.34111504
 [17,] -0.95647033
 [18,] -0.26044656
 [19,] -1.74407616
 [20,]  0.38062795
 [21,] -1.12131806
 [22,] -1.13963448
 [23,] -1.46932994
 [24,] -1.04805240
 [25,] -0.93815391
 [26,] -1.57922843
 [27,] -0.60845845
 [28,] -0.62677486
 [29,] -1.10300165
 [30,] -0.62677486
 [31,] -0.80993901
 [32,] -1.23121655
 [33,] -0.80993901
 [34,] -0.55350920
 [35,] -1.37774787
 [36,] -0.86488825
 [37,] -0.93815391
 [38,] -0.31539581
 [39,] -1.15795089
 [40,] -0.75498976
 [41,] -1.35943145
 [42,] -0.57182562
 [43,] -1.45101353
 [44,]  0.03261607
 [45,] -1.26784938
 [46,] -0.79162259
 [47,] -0.51687637
 [48,] -1.17626731
 [49,] -1.45101353
 [50,] -0.29707939
 [51,] -0.79162259
 [52,] -0.70004052
 [53,] -1.63417768
 [54,] -0.35202864
 [55,] -1.72575975
 [56,] -0.46192713
 [57,] -0.90152108
 [58,] -0.60845845
 [59,] -1.35943145
 [60,] -1.15795089
 [61,] -1.50596277
 [62,] -0.48024354
 [63,] -1.15795089
 [64,] -0.51687637
 [65,] -1.37774787
 [66,] -0.42529430
 [67,] -1.54259560
 [68,] -0.51687637
 [69,] -1.46932994
 [70,] -0.38866147
 [71,] -1.90892390
 [72,] -0.77330618
 [73,] -0.79162259
 [74,]  0.34399512
 [75,] -1.54259560
 [76,] -0.20549732
 [77,] -0.55350920
 [78,] -1.23121655
 [79,] -1.41438070
 [80,] -0.33371222
 [81,] -1.70744334
 [82,] -0.18718091
 [83,] -1.32279862
 [84,] -1.61586126
 [85,] -1.21290014
 [86,] -0.48024354
 [87,] -1.39606428
 [88,] -1.28616579
 [89,] -1.02973599
 [90,] -0.91983750
 [91,] -1.50596277
 [92,] -0.51687637
 [93,] -1.81734182
 [94,] -0.79162259
 [95,] -1.41438070
 [96,] -0.57182562
 [97,] -1.06636882
 [98,] -0.66340769
 [99,] -1.98218956
[100,] -0.13223166
[101,] -1.63417768
[102,] -0.53519279
[103,] -1.13963448
[104,] -1.12131806
[105,] -1.10300165
[106,] -0.77330618
[107,] -0.97478674
[108,] -1.04805240
[109,] -1.06636882
[110,] -0.13223166
[111,] -1.06636882
[112,]  0.30736229
[113,] -0.77330618
[114,] -0.31539581
[115,] -0.79162259
[116,] -0.22381374
[117,] -0.97478674
[118,] -1.21290014
[119,] -1.50596277
[120,] -0.51687637
[121,] -1.41438070
[122,] -1.13963448
[123,] -0.68172411
[124,] -0.46192713
[125,] -1.59754485
[126,] -0.60845845
[127,] -0.93815391
[128,] -0.44361071
[129,] -0.90152108
[130,]  0.03261607
[131,] -0.99310316
[132,] -0.15054808
[133,] -1.30448221
[134,] -1.17626731
[135,] -1.06636882
[136,] -0.51687637
[137,] -1.52427919
[138,] -0.68172411
[139,] -1.26784938
[140,] -0.77330618
[141,] -0.68172411
[142,] -0.60845845
[143,] -2.16535371
[144,] -0.59014203
[145,] -1.21290014
[146,] -0.90152108
[147,] -0.86488825
[148,] -1.34111504
[149,] -1.45101353
[150,] -1.12131806
[151,] -1.45101353
[152,] -0.44361071
[153,]  0.39894437
[154,]  1.11328455
[155,]  0.87517115
[156,]  1.11328455
[157,]  0.67369059
[158,]  0.47221003
[159,]  0.27072946
[160,]  0.50884286
[161,] -0.11391525
[162,]  0.52715927
[163,] -0.55350920
[164,]  0.93012040
[165,]  0.28904588
[166,]  0.82022191
[167,]  0.34399512
[168,]  0.98506964
[169,] -0.35202864
[170,]  0.96675323
[171,]  0.41726078
[172,]  0.87517115
[173,]  1.14991738
[174,]  0.21578022
[175,]  0.47221003
[176,]  0.43557720
[177,] -0.18718091
[178,]  0.39894437
[179,]  0.10588173
[180,]  0.71032342
[181,]  0.78358908
[182,]  1.11328455
[183,]  0.61874135
[184,] -0.20549732
[185,]  0.21578022
[186,]  2.87166037
[187,]  0.94843681
[188,]  0.82022191
[189,] -0.24213015
[190,]  0.08756532
[191,]  0.01429966
[192,]  0.87517115
[193,] -0.22381374
[194,]  1.04001889
[195,]  0.25241305
[196,]  1.04001889
[197,]  1.20486662
[198,] -0.05896600
[199,]  0.28904588
[200,]  1.20486662
[201,]  0.17914739
[202,]  0.23409663
[203,]  0.49052644
[204,]  0.83853832
[205,]  0.21578022
[206,]  1.13160096
[207,]  0.47221003
[208,]  0.19746381
[209,] -0.02233317
[210,]  0.28904588
[211,] -0.13223166
[212,]  1.18655021
[213,]  0.25241305
[214,]  0.41726078
[215,]  0.32567871
[216,]  1.90089038
[217,]  0.34399512
[218,]  1.07665172
[219,]  0.41726078
[220,]  1.02170247
[221,] -0.07728242
[222,]  1.24149945
[223,]  0.69200701
[224,]  0.45389361
[225,]  0.78358908
[226,]  0.47221003
[227,]  0.45389361
[228,]  0.85685474
[229,]  0.65537418
[230,]  1.31476511
[231,]  0.23409663
[232,]  0.23409663
[233,]  0.94843681
[234,]  1.57119492
[235,]  0.63705776
[236,]  1.11328455
[237,]  0.17914739
[238,]  1.25981586
[239,] -0.09559883
[240,]  1.35139794
[241,]  0.65537418
[242,]  1.49792926
[243,]  0.65537418
[244,]  1.51624567
[245,]  0.28904588
[246,]  1.02170247
[247,]  0.10588173
[248,]  1.25981586
[249,]  1.00338606
[250,]  0.54547569
[251,]  0.82022191
[252,]  1.31476511
[253,]  0.83853832
[254,]  2.19395302
[255,]  0.60042493
[256,]  0.94843681
[257,]  0.61874135
[258,]  0.52715927
[259,] -0.40697788
[260,]  1.73604265
[261,] -0.11391525
[262,]  0.76527266
[263,]  1.20486662
[264,]  1.07665172
[265,] -0.07728242
[266,]  1.38803077
[267,]  0.41726078
[268,]  2.04742170
[269,]  0.10588173
[270,]  0.89348757
[271,]  0.60042493
[272,]          NA
[273,]  0.52715927
[274,]  1.18655021
[275,]  0.23409663
[276,]  1.09496813
[277,]  0.47221003
[278,]  1.11328455
[279,]  1.35139794
[280,]  0.27072946
[281,]  1.60782775
[282,]  0.23409663
[283,]  0.39894437
[284,]  1.35139794
[285,]  0.38062795
[286,]  1.35139794
[287,]  0.49052644
[288,]  1.42466360
[289,]  0.56379210
[290,]  1.47961284
[291,]  0.36231154
[292,]  1.20486662
[293,]  1.16823379
[294,]  2.57859773
[295,]  0.45389361
[296,]  0.96675323
[297,] -0.27876298
[298,]  0.83853832
[299,] -0.13223166
[300,]  1.22318303
[301,]  0.50884286
[302,]  1.47961284
[303,]  1.20486662
[304,]  1.02170247
[305,]  0.45389361
[306,]  1.62614416
[307,] -0.55350920
[308,]  1.88257397
[309,] -0.26044656
[310,]  1.29644869
[311,]  1.05833530
[312,]  0.65537418
[313,]  0.67369059
[314,]  1.47961284
[315,]  0.54547569
[316,]  1.75435906
[317,]  0.93012040
[318,]  0.41726078
[319,]  1.27813228
[320,]  0.28904588
[321,]  1.27813228
[322,]  1.25981586
[323,]  1.13160096
[324,]  0.93012040
[325,]  1.38803077
[326,]  1.07665172
[327,]  0.76527266
[328,]  1.36971435
[329,]  0.32567871
[330,]  1.24149945
[331,] -0.26044656
[332,]  1.51624567
[333,]  0.23409663
[334,]  0.98506964
[335,]  1.14991738
[336,]  0.30736229
[337,]  1.46129643
[338,]  0.52715927
[339,]  0.32567871
[340,]  2.17563660
[341,] -0.07728242
[342,]  1.04001889
[343,]  1.25981586
[344,]  1.14991738
attr(,"scaled:center")
[1] 43.92193
attr(,"scaled:scale")
[1] 5.459584

$bill_depth_mm
              [,1]
  [1,]  0.78430007
  [2,]  0.12600328
  [3,]  0.42983257
  [4,]          NA
  [5,]  1.08812936
  [6,]  1.74642615
  [7,]  0.32855614
  [8,]  1.24004400
  [9,]  0.48047078
 [10,]  1.54387329
 [11,] -0.02591137
 [12,]  0.07536506
 [13,]  0.22727971
 [14,]  2.05025544
 [15,]  1.99961722
 [16,]  0.32855614
 [17,]  0.93621471
 [18,]  1.79706436
 [19,]  0.63238542
 [20,]  2.20217008
 [21,]  0.58174721
 [22,]  0.78430007
 [23,]  1.03749114
 [24,]  0.48047078
 [25,]  0.02472685
 [26,]  0.88557650
 [27,]  0.73366185
 [28,]  0.37919435
 [29,]  0.73366185
 [30,]  0.88557650
 [31,] -0.22846423
 [32,]  0.48047078
 [33,]  0.32855614
 [34,]  0.88557650
 [35,] -0.07654958
 [36,]  1.99961722
 [37,]  1.44259686
 [38,]  0.68302364
 [39,]  1.08812936
 [40,]  0.98685293
 [41,]  0.42983257
 [42,]  0.63238542
 [43,]  0.68302364
 [44,]  1.29068222
 [45,] -0.12718780
 [46,]  0.83493828
 [47,]  0.93621471
 [48,]  0.88557650
 [49,]  0.37919435
 [50,]  2.05025544
 [51,]  0.27791792
 [52,]  0.88557650
 [53,]  0.37919435
 [54,]  1.18940579
 [55,]  0.48047078
 [56,]  0.73366185
 [57,]  0.17664149
 [58,]  0.83493828
 [59,] -0.27910244
 [60,]  0.98685293
 [61,] -0.12718780
 [62,]  1.99961722
 [63,] -0.07654958
 [64,]  0.53110900
 [65,] -0.02591137
 [66,]  0.42983257
 [67,] -0.48165530
 [68,]  0.98685293
 [69,] -0.27910244
 [70,]  1.13876757
 [71,]  0.93621471
 [72,]  0.63238542
 [73,]  0.02472685
 [74,]  0.88557650
 [75,]  0.17664149
 [76,]  0.68302364
 [77,] -0.17782601
 [78,]  1.13876757
 [79,] -0.53229351
 [80,]  0.98685293
 [81,]  0.02472685
 [82,]  0.22727971
 [83,]  0.83493828
 [84,]  1.13876757
 [85,]  0.32855614
 [86,]  1.59451151
 [87,]  1.18940579
 [88,]  0.73366185
 [89,]  1.03749114
 [90,]  0.83493828
 [91,]  0.42983257
 [92,]  0.48047078
 [93,] -0.02591137
 [94,]  0.48047078
 [95,]  0.07536506
 [96,]  0.88557650
 [97,]  0.73366185
 [98,]  0.68302364
 [99,] -0.53229351
[100,]  0.68302364
[101,]  0.37919435
[102,]  1.44259686
[103,] -0.58293173
[104,]  1.44259686
[105,]  0.73366185
[106,]  0.88557650
[107,]  0.02472685
[108,]  1.44259686
[109,] -0.07654958
[110,]  0.93621471
[111,] -0.32974066
[112,]  1.59451151
[113,]  0.27791792
[114,]  1.18940579
[115,]  1.79706436
[116,]  0.58174721
[117,] -0.07654958
[118,]  1.69578793
[119,] -0.07654958
[120,]  0.73366185
[121,]  0.02472685
[122,]  1.34132043
[123,] -0.07654958
[124,]  0.68302364
[125,] -0.63356994
[126,]  0.93621471
[127,]  0.22727971
[128,]  0.58174721
[129,] -0.02591137
[130,]  0.42983257
[131,]  0.37919435
[132,]  1.03749114
[133,]  0.68302364
[134,]  0.68302364
[135,]  0.22727971
[136,]  0.17664149
[137,]  0.17664149
[138,]  1.49323508
[139,] -0.32974066
[140,]  0.37919435
[141,] -0.02591137
[142,]  0.02472685
[143,] -0.83612280
[144,] -0.07654958
[145,] -0.17782601
[146,]  0.78430007
[147,]  0.73366185
[148,]  0.63238542
[149,]  0.32855614
[150,]  0.48047078
[151,] -0.02591137
[152,]  0.68302364
[153,] -2.00080174
[154,] -0.43101709
[155,] -1.54505781
[156,] -0.98803745
[157,] -1.34250495
[158,] -1.84888710
[159,] -1.29186674
[160,] -0.93739923
[161,] -1.89952531
[162,] -0.88676102
[163,] -1.74761067
[164,] -0.53229351
[165,] -1.74761067
[166,] -1.29186674
[167,] -1.29186674
[168,] -0.73484637
[169,] -1.84888710
[170,] -0.98803745
[171,] -1.34250495
[172,] -1.03867566
[173,] -1.44378138
[174,] -1.34250495
[175,] -1.34250495
[176,] -0.68420816
[177,] -2.05143996
[178,] -1.03867566
[179,] -1.44378138
[180,] -1.08931388
[181,] -1.44378138
[182,] -0.93739923
[183,] -0.93739923
[184,] -1.49441960
[185,] -1.34250495
[186,] -0.07654958
[187,] -1.19059031
[188,] -0.43101709
[189,] -1.74761067
[190,]  0.07536506
[191,] -1.79824888
[192,] -0.73484637
[193,] -1.74761067
[194,] -0.58293173
[195,] -1.74761067
[196,] -1.08931388
[197,] -0.63356994
[198,] -1.64633424
[199,] -1.64633424
[200,] -0.63356994
[201,] -1.95016353
[202,] -0.68420816
[203,] -1.49441960
[204,] -1.54505781
[205,] -1.39314317
[206,] -1.08931388
[207,] -1.39314317
[208,] -0.88676102
[209,] -1.64633424
[210,] -1.08931388
[211,] -1.34250495
[212,] -0.93739923
[213,] -1.69697245
[214,] -1.13995209
[215,] -1.64633424
[216,] -0.73484637
[217,] -1.49441960
[218,] -0.17782601
[219,] -1.39314317
[220,] -0.48165530
[221,] -1.49441960
[222,] -1.08931388
[223,] -1.08931388
[224,] -0.78548459
[225,] -0.78548459
[226,] -1.19059031
[227,] -1.08931388
[228,] -0.58293173
[229,] -1.49441960
[230,] -0.43101709
[231,] -1.69697245
[232,] -0.38037887
[233,] -1.34250495
[234,] -0.78548459
[235,] -1.29186674
[236,] -0.63356994
[237,] -1.69697245
[238,]  0.07536506
[239,] -1.39314317
[240,] -1.49441960
[241,] -1.59569603
[242,] -0.07654958
[243,] -1.08931388
[244,] -0.02591137
[245,] -1.34250495
[246,] -0.53229351
[247,] -1.24122852
[248,] -0.73484637
[249,] -0.68420816
[250,] -1.29186674
[251,] -1.39314317
[252,] -0.32974066
[253,] -1.08931388
[254,] -0.07654958
[255,] -0.83612280
[256,] -1.08931388
[257,] -1.69697245
[258,] -0.53229351
[259,] -1.24122852
[260,] -0.68420816
[261,] -1.59569603
[262,] -1.03867566
[263,] -0.98803745
[264,] -0.63356994
[265,] -0.98803745
[266,] -0.43101709
[267,] -1.54505781
[268,] -0.58293173
[269,] -0.73484637
[270,] -0.48165530
[271,] -1.74761067
[272,]          NA
[273,] -1.44378138
[274,] -0.73484637
[275,] -1.19059031
[276,] -0.53229351
[277,]  0.37919435
[278,]  1.18940579
[279,]  1.03749114
[280,]  0.78430007
[281,]  1.34132043
[282,]  0.32855614
[283,]  0.53110900
[284,]  0.53110900
[285,]  0.88557650
[286,]  1.39195865
[287,]  0.32855614
[288,]  1.59451151
[289,]  0.07536506
[290,]  0.48047078
[291,] -0.02591137
[292,]  1.24004400
[293,]  1.44259686
[294,]  0.32855614
[295,]  0.73366185
[296,]  0.53110900
[297,]  0.07536506
[298,]  0.17664149
[299,] -0.27910244
[300,]  1.13876757
[301,]  0.37919435
[302,]  0.93621471
[303,]  0.63238542
[304,]  0.93621471
[305,]  0.32855614
[306,]  1.44259686
[307,] -0.27910244
[308,]  1.84770258
[309,] -0.22846423
[310,]  0.83493828
[311,]  0.73366185
[312,] -0.17782601
[313,]  0.58174721
[314,]  1.79706436
[315,] -0.27910244
[316,]  1.39195865
[317,]  1.18940579
[318,]  0.17664149
[319,]  0.98685293
[320,] -0.07654958
[321,]  0.37919435
[322,]  0.68302364
[323,]  0.37919435
[324,]  1.24004400
[325,]  0.78430007
[326,]  0.07536506
[327,] -0.38037887
[328,]  0.93621471
[329,]  0.07536506
[330,]  1.29068222
[331,]  0.07536506
[332,]  0.83493828
[333,] -0.27910244
[334,]  1.39195865
[335,]  0.83493828
[336,]  1.13876757
[337,]  1.18940579
[338,] -0.32974066
[339,] -0.07654958
[340,]  1.34132043
[341,]  0.48047078
[342,]  0.53110900
[343,]  0.93621471
[344,]  0.78430007
attr(,"scaled:center")
[1] 17.15117
attr(,"scaled:scale")
[1] 1.974793

$flipper_length_mm
               [,1]
  [1,] -1.416271525
  [2,] -1.060696087
  [3,] -0.420660299
  [4,]           NA
  [5,] -0.562890474
  [6,] -0.776235737
  [7,] -1.416271525
  [8,] -0.420660299
  [9,] -0.562890474
 [10,] -0.776235737
 [11,] -1.060696087
 [12,] -1.487386613
 [13,] -1.345156438
 [14,] -0.705120649
 [15,] -0.207315036
 [16,] -1.131811175
 [17,] -0.420660299
 [18,] -0.278430124
 [19,] -1.202926262
 [20,] -0.491775386
 [21,] -1.914077138
 [22,] -1.487386613
 [23,] -0.847350824
 [24,] -1.131811175
 [25,] -1.487386613
 [26,] -0.989581000
 [27,] -1.274041350
 [28,] -0.989581000
 [29,] -2.056307313
 [30,] -1.487386613
 [31,] -1.629616788
 [32,] -1.629616788
 [33,] -0.918465912
 [34,] -1.202926262
 [35,] -0.420660299
 [36,] -0.349545211
 [37,] -0.776235737
 [38,] -1.487386613
 [39,] -1.416271525
 [40,] -1.202926262
 [41,] -1.345156438
 [42,] -0.420660299
 [43,] -1.060696087
 [44,] -0.349545211
 [45,] -1.131811175
 [46,] -0.776235737
 [47,] -1.345156438
 [48,] -1.558501700
 [49,] -0.776235737
 [50,] -0.705120649
 [51,] -1.060696087
 [52,] -0.918465912
 [53,] -0.776235737
 [54,] -0.065084861
 [55,] -0.989581000
 [56,] -0.705120649
 [57,] -1.060696087
 [58,] -0.562890474
 [59,] -1.416271525
 [60,] -0.491775386
 [61,] -1.131811175
 [62,] -0.420660299
 [63,] -1.131811175
 [64,] -0.634005562
 [65,] -1.202926262
 [66,] -0.634005562
 [67,] -0.420660299
 [68,] -0.918465912
 [69,] -0.776235737
 [70,] -0.207315036
 [71,] -0.776235737
 [72,] -0.776235737
 [73,] -0.349545211
 [74,] -0.278430124
 [75,] -0.776235737
 [76,] -0.420660299
 [77,] -0.705120649
 [78,] -1.202926262
 [79,] -0.989581000
 [80,] -0.420660299
 [81,] -0.847350824
 [82,] -0.349545211
 [83,] -0.989581000
 [84,] -0.562890474
 [85,] -0.705120649
 [86,] -0.491775386
 [87,] -0.776235737
 [88,] -0.847350824
 [89,] -0.847350824
 [90,] -0.776235737
 [91,]  0.077145314
 [92,]  0.290490577
 [93,] -1.131811175
 [94,] -1.060696087
 [95,] -0.989581000
 [96,]  0.503835840
 [97,] -0.776235737
 [98,] -0.349545211
 [99,] -1.629616788
[100,] -0.634005562
[101,] -0.634005562
[102,]  0.148260402
[103,] -1.274041350
[104,] -0.776235737
[105,] -0.562890474
[106,] -1.202926262
[107,] -0.136199948
[108,] -0.776235737
[109,] -1.416271525
[110,] -0.278430124
[111,] -0.207315036
[112,] -0.705120649
[113,] -0.562890474
[114,] -0.278430124
[115,] -0.705120649
[116,] -0.349545211
[117,] -0.918465912
[118,] -0.136199948
[119,] -0.847350824
[120,] -0.847350824
[121,] -0.989581000
[122,] -0.207315036
[123,] -1.771846963
[124,]  0.077145314
[125,] -1.060696087
[126,] -0.136199948
[127,] -0.705120649
[128,] -0.420660299
[129,] -0.705120649
[130,]  0.646066015
[131,] -0.776235737
[132,] -0.278430124
[133,] -0.562890474
[134,] -0.136199948
[135,] -0.989581000
[136,] -0.776235737
[137,] -0.705120649
[138,] -0.065084861
[139,] -1.131811175
[140,] -0.562890474
[141,] -0.562890474
[142,] -0.989581000
[143,] -0.918465912
[144,] -0.776235737
[145,] -0.634005562
[146,] -1.131811175
[147,] -0.776235737
[148,] -1.202926262
[149,] -0.420660299
[150,] -0.562890474
[151,] -0.989581000
[152,]  0.006030227
[153,]  0.717181103
[154,]  2.068367767
[155,]  0.646066015
[156,]  1.214986716
[157,]  1.001641453
[158,]  0.646066015
[159,]  0.717181103
[160,]  1.286101803
[161,]  0.574950927
[162,]  1.001641453
[163,]  0.930526365
[164,]  1.072756541
[165,]  0.930526365
[166,]  0.859411278
[167,]  0.646066015
[168,]  1.143871628
[169,]  0.646066015
[170,]  1.428331979
[171,]  0.574950927
[172,]  1.499447066
[173,]  1.214986716
[174,]  1.001641453
[175,]  0.859411278
[176,]  1.001641453
[177,]  1.001641453
[178,]  1.001641453
[179,]  1.072756541
[180,]  1.001641453
[181,]  0.646066015
[182,]  1.357216891
[183,]  1.499447066
[184,]  0.574950927
[185,]  0.432720752
[186,]  2.068367767
[187,]  1.357216891
[188,]  1.357216891
[189,]  0.859411278
[190,]  1.286101803
[191,]  0.503835840
[192,]  0.503835840
[193,]  0.503835840
[194,]  1.712792329
[195,]  0.646066015
[196,]  1.072756541
[197,]  1.499447066
[198,]  1.143871628
[199,]  0.646066015
[200,]  1.712792329
[201,]  0.859411278
[202,]  1.001641453
[203,]  0.646066015
[204,]  1.357216891
[205,]  0.646066015
[206,]  1.712792329
[207,]  1.143871628
[208,]  1.357216891
[209,]  0.503835840
[210,]  1.357216891
[211,]  0.503835840
[212,]  1.641677241
[213,]  0.503835840
[214,]  1.428331979
[215,]  0.930526365
[216,]  2.139482854
[217,]  1.286101803
[218,]  2.068367767
[219,]  0.930526365
[220,]  1.997252679
[221,]  1.357216891
[222,]  1.570562154
[223,]  1.072756541
[224,]  1.428331979
[225,]  1.428331979
[226,]  1.143871628
[227,]  1.072756541
[228,]  2.068367767
[229,]  0.574950927
[230,]  1.357216891
[231,]  1.001641453
[232,]  1.570562154
[233,]  0.788296190
[234,]  1.428331979
[235,]  0.788296190
[236,]  1.641677241
[237,]  0.788296190
[238,]  1.926137592
[239,]  1.214986716
[240,]  1.214986716
[241,]  0.788296190
[242,]  2.068367767
[243,]  1.214986716
[244,]  1.926137592
[245,]  0.788296190
[246,]  1.641677241
[247,]  0.930526365
[248,]  1.783907417
[249,]  1.072756541
[250,]  1.499447066
[251,]  0.148260402
[252,]  1.712792329
[253,]  1.286101803
[254,]  1.926137592
[255,]  1.001641453
[256,]  1.926137592
[257,]  1.072756541
[258,]  1.001641453
[259,]  0.646066015
[260,]  1.286101803
[261,]  0.503835840
[262,]  0.574950927
[263,]  1.072756541
[264,]  1.997252679
[265,]  0.859411278
[266,]  2.068367767
[267,]  1.143871628
[268,]  2.068367767
[269,]  1.143871628
[270,]  1.499447066
[271,]  0.930526365
[272,]           NA
[273,]  1.001641453
[274,]  1.499447066
[275,]  0.788296190
[276,]  0.859411278
[277,] -0.634005562
[278,] -0.349545211
[279,] -0.562890474
[280,] -0.918465912
[281,] -0.278430124
[282,] -0.207315036
[283,] -1.629616788
[284,] -0.278430124
[285,] -0.420660299
[286,] -0.207315036
[287,] -0.562890474
[288,] -0.491775386
[289,] -1.131811175
[290,]  0.006030227
[291,] -0.776235737
[292,]  0.006030227
[293,] -0.278430124
[294,] -1.416271525
[295,] -0.776235737
[296,] -0.420660299
[297,] -1.416271525
[298,] -0.705120649
[299,] -0.989581000
[300,] -0.562890474
[301,] -0.420660299
[302,] -0.278430124
[303,] -0.065084861
[304,] -0.065084861
[305,] -0.705120649
[306,]  0.290490577
[307,] -0.989581000
[308,]  0.006030227
[309,] -0.989581000
[310,]  0.148260402
[311,] -0.420660299
[312,] -0.136199948
[313,] -0.420660299
[314,]  0.646066015
[315,] -0.634005562
[316,]  0.290490577
[317,]  0.646066015
[318,] -0.989581000
[319,] -0.349545211
[320,] -0.349545211
[321,] -0.349545211
[322,]  0.006030227
[323,] -0.776235737
[324,]  0.788296190
[325,] -0.989581000
[326,] -0.207315036
[327,] -0.136199948
[328,]  0.006030227
[329,] -0.562890474
[330,]  0.148260402
[331,] -0.989581000
[332,] -0.278430124
[333,] -0.705120649
[334,]  0.148260402
[335,]  0.077145314
[336,] -0.491775386
[337,]  0.361605665
[338,] -0.847350824
[339,] -0.420660299
[340,]  0.432720752
[341,]  0.077145314
[342,] -0.562890474
[343,]  0.646066015
[344,] -0.207315036
attr(,"scaled:center")
[1] 200.9152
attr(,"scaled:scale")
[1] 14.06171

$body_mass_g
               [,1]
  [1,] -0.563316704
  [2,] -0.500969030
  [3,] -1.186793445
  [4,]           NA
  [5,] -0.937402749
  [6,] -0.688012052
  [7,] -0.719185889
  [8,]  0.590115266
  [9,] -0.906228912
 [10,]  0.060160036
 [11,] -1.124445771
 [12,] -0.625664378
 [13,] -1.249141119
 [14,] -0.500969030
 [15,]  0.247203059
 [16,] -0.625664378
 [17,] -0.937402749
 [18,]  0.371898407
 [19,] -1.093271934
 [20,] -0.002187638
 [21,] -0.999750423
 [22,] -0.750359726
 [23,] -0.500969030
 [24,] -0.313926008
 [25,] -0.500969030
 [26,] -0.500969030
 [27,] -0.812707400
 [28,] -1.249141119
 [29,] -1.311488793
 [30,] -0.313926008
 [31,] -1.186793445
 [32,] -0.376273682
 [33,] -1.124445771
 [34,] -0.376273682
 [35,] -1.093271934
 [36,] -0.064535312
 [37,] -0.313926008
 [38,] -0.812707400
 [39,] -1.124445771
 [40,]  0.558941429
 [41,] -1.311488793
 [42,] -0.376273682
 [43,] -1.373836467
 [44,]  0.247203059
 [45,] -1.498531815
 [46,]  0.496593755
 [47,] -0.968576586
 [48,] -1.529705652
 [49,] -0.937402749
 [50,] -0.064535312
 [51,] -0.875055074
 [52,]  0.122507710
 [53,] -0.937402749
 [54,] -0.189230660
 [55,] -1.623227163
 [56,] -0.625664378
 [57,] -0.812707400
 [58,] -0.500969030
 [59,] -1.685574837
 [60,] -0.563316704
 [61,] -1.311488793
 [62,]  0.247203059
 [63,] -0.750359726
 [64,] -0.189230660
 [65,] -1.685574837
 [66,] -0.313926008
 [67,] -1.062098097
 [68,] -0.126882986
 [69,] -1.436184141
 [70,]  0.309550733
 [71,] -0.750359726
 [72,] -0.376273682
 [73,] -0.812707400
 [74,] -0.064535312
 [75,] -0.625664378
 [76,]  0.060160036
 [77,] -0.625664378
 [78,] -0.376273682
 [79,] -0.812707400
 [80,] -0.251578334
 [81,] -1.249141119
 [82,]  0.621289103
 [83,] -0.500969030
 [84,] -0.002187638
 [85,] -1.062098097
 [86,] -0.812707400
 [87,] -0.500969030
 [88,] -0.875055074
 [89,] -0.313926008
 [90,] -0.750359726
 [91,] -0.812707400
 [92,]  0.122507710
 [93,] -0.999750423
 [94,]  0.309550733
 [95,] -1.124445771
 [96,]  0.122507710
 [97,] -0.625664378
 [98,]  0.184855384
 [99,] -1.623227163
[100,] -0.126882986
[101,] -0.594490541
[102,]  0.652462940
[103,] -1.405010304
[104,]  0.060160036
[105,] -1.592053326
[106,] -0.812707400
[107,] -0.563316704
[108,] -0.376273682
[109,] -1.280314956
[110,]  0.714810614
[111,] -0.469795193
[112,]  0.496593755
[113,] -1.249141119
[114,]  0.091333873
[115,] -0.376273682
[116,] -0.158056823
[117,] -1.623227163
[118,] -0.532142867
[119,] -1.062098097
[120,] -1.093271934
[121,] -1.311488793
[122,] -0.875055074
[123,] -0.937402749
[124,] -0.407447519
[125,] -1.436184141
[126,] -0.251578334
[127,] -1.155619608
[128,]  0.122507710
[129,] -1.436184141
[130,] -0.251578334
[131,] -1.093271934
[132,] -0.875055074
[133,] -0.875055074
[134,]  0.340724570
[135,] -0.968576586
[136,] -0.376273682
[137,] -1.280314956
[138,] -0.282752171
[139,] -0.999750423
[140,]  0.060160036
[141,] -0.999750423
[142,] -0.906228912
[143,] -1.436184141
[144,] -0.594490541
[145,] -1.498531815
[146,] -0.688012052
[147,]  0.060160036
[148,] -0.906228912
[149,] -0.937402749
[150,] -0.563316704
[151,] -0.625664378
[152,] -0.251578334
[153,]  0.371898407
[154,]  1.868242584
[155,]  0.309550733
[156,]  1.868242584
[157,]  1.494156540
[158,]  0.434246081
[159,]  0.745984451
[160,]  1.244765843
[161,]  0.247203059
[162,]  1.182418169
[163,]  0.558941429
[164,]  1.681199562
[165,]  0.558941429
[166,]  2.055285606
[167,] -0.002187638
[168,]  2.055285606
[169,] -0.064535312
[170,]  2.616414673
[171,]  0.745984451
[172,]  1.431808866
[173,]  1.868242584
[174,]  0.995375147
[175,]  0.247203059
[176,]  1.057722821
[177,]  0.995375147
[178,]  1.120070495
[179,] -0.126882986
[180,]  1.805894910
[181,]  0.496593755
[182,]  1.681199562
[183,]  1.307113518
[184,]  0.621289103
[185,]  1.057722821
[186,]  2.304676302
[187,]  1.182418169
[188,]  1.494156540
[189,]  0.933027473
[190,]  1.307113518
[191,]  0.184855384
[192,]  1.431808866
[193,] -0.313926008
[194,]  1.868242584
[195,]  0.122507710
[196,]  0.683636777
[197,]  1.681199562
[198,]  0.870679799
[199,] -0.002187638
[200,]  1.494156540
[201,]  1.120070495
[202,]  1.369461192
[203,]  0.808332125
[204,]  1.369461192
[205,]  0.247203059
[206,]  0.995375147
[207,]  0.870679799
[208,]  1.057722821
[209,]  0.122507710
[210,]  0.995375147
[211,]  0.309550733
[212,]  1.681199562
[213,] -0.002187638
[214,]  1.369461192
[215,]  0.247203059
[216,]  1.805894910
[217,]  0.621289103
[218,]  1.868242584
[219,]  0.558941429
[220,]  1.992937932
[221,]  0.621289103
[222,]  1.681199562
[223,]  0.683636777
[224,]  0.995375147
[225,]  1.120070495
[226,]  1.244765843
[227,]  0.621289103
[228,]  1.992937932
[229,]  0.496593755
[230,]  2.242328628
[231,]  0.683636777
[232,]  2.179980954
[233,]  0.527767592
[234,]  1.556504214
[235,]  0.652462940
[236,]  1.431808866
[237,]  0.683636777
[238,]  1.743547236
[239,]  0.496593755
[240,]  1.369461192
[241,]  0.839505962
[242,]  1.681199562
[243,]  0.933027473
[244,]  1.494156540
[245,]  0.683636777
[246,]  1.805894910
[247,]  0.808332125
[248,]  1.244765843
[249,]  0.901853636
[250,]  0.839505962
[251,]  0.527767592
[252,]  1.307113518
[253,]  0.808332125
[254,]  1.743547236
[255,]  0.964201310
[256,]  1.618851888
[257,]  0.652462940
[258,]  1.618851888
[259,]  0.621289103
[260,]  1.618851888
[261,]  0.465419918
[262,]  1.618851888
[263,]  0.995375147
[264,]  2.179980954
[265,]  0.558941429
[266,]  1.618851888
[267,]  0.216029222
[268,]  2.055285606
[269,]  0.839505962
[270,]  2.242328628
[271,]  0.901853636
[272,]           NA
[273,]  0.808332125
[274,]  1.930590258
[275,]  1.244765843
[276,]  1.494156540
[277,] -0.875055074
[278,] -0.376273682
[279,] -0.688012052
[280,] -0.843881237
[281,] -0.594490541
[282,] -0.313926008
[283,] -1.186793445
[284,] -0.563316704
[285,] -0.064535312
[286,] -0.625664378
[287,] -0.500969030
[288,] -0.532142867
[289,] -0.625664378
[290,] -0.189230660
[291,] -0.781533563
[292,] -0.189230660
[293,] -1.124445771
[294,] -0.625664378
[295,] -0.937402749
[296,]  0.247203059
[297,] -0.750359726
[298,] -0.999750423
[299,] -1.623227163
[300,] -0.500969030
[301,] -1.124445771
[302,] -0.064535312
[303,] -0.999750423
[304,] -0.500969030
[305,] -0.625664378
[306,]  0.434246081
[307,] -1.249141119
[308,]  0.122507710
[309,] -1.062098097
[310,] -0.126882986
[311,] -0.750359726
[312,] -0.376273682
[313,] -0.438621356
[314,]  0.745984451
[315,] -1.872617859
[316,]  0.371898407
[317,] -0.313926008
[318,] -0.688012052
[319,] -0.812707400
[320,] -0.875055074
[321,] -0.656838215
[322,]  0.309550733
[323,] -0.999750423
[324,]  0.122507710
[325,] -1.186793445
[326,] -0.656838215
[327,] -1.093271934
[328,] -0.313926008
[329,] -0.750359726
[330,] -0.189230660
[331,] -1.062098097
[332,] -0.937402749
[333,] -1.186793445
[334,] -0.189230660
[335,] -0.500969030
[336,] -0.843881237
[337,] -0.313926008
[338,] -0.688012052
[339,] -0.688012052
[340,] -0.251578334
[341,] -0.999750423
[342,] -0.532142867
[343,] -0.126882986
[344,] -0.532142867
attr(,"scaled:center")
[1] 4201.754
attr(,"scaled:scale")
[1] 801.9545

$sex
  [1] male   female female <NA>   female male   female male   <NA>   <NA>  
 [11] <NA>   <NA>   female male   male   female female male   female male  
 [21] female male   female male   male   female male   female female male  
 [31] female male   female male   female male   male   female female male  
 [41] female male   female male   female male   male   <NA>   female male  
 [51] female male   female male   female male   female male   female male  
 [61] female male   female male   female male   female male   female male  
 [71] female male   female male   female male   female male   female male  
 [81] female male   female male   female male   male   female male   female
 [91] female male   female male   female male   female male   female male  
[101] female male   female male   female male   female male   female male  
[111] female male   female male   female male   female male   female male  
[121] female male   female male   female male   female male   female male  
[131] female male   female male   female male   female male   female male  
[141] female male   female male   female male   male   female female male  
[151] female male   female male   female male   male   female female male  
[161] female male   female male   female male   female male   female male  
[171] female male   male   female female male   female male   <NA>   male  
[181] female male   male   female female male   female male   female male  
[191] female male   female male   female male   male   female female male  
[201] female male   female male   female male   female male   female male  
[211] female male   female male   female male   female male   <NA>   male  
[221] female male   female male   male   female female male   female male  
[231] female male   female male   female male   female male   female male  
[241] female male   female male   female male   female male   male   female
[251] female male   female male   female male   <NA>   male   female male  
[261] female male   female male   female male   female male   <NA>   male  
[271] female <NA>   female male   female male   female male   male   female
[281] male   female female male   female male   female male   female male  
[291] female male   male   female female male   female male   female male  
[301] female male   female male   female male   female male   female male  
[311] male   female female male   female male   male   female male   female
[321] female male   female male   male   female female male   female male  
[331] female male   female male   male   female male   female female male  
[341] female male   male   female
Levels: female male

$year
              [,1]
  [1,] -1.25748435
  [2,] -1.25748435
  [3,] -1.25748435
  [4,] -1.25748435
  [5,] -1.25748435
  [6,] -1.25748435
  [7,] -1.25748435
  [8,] -1.25748435
  [9,] -1.25748435
 [10,] -1.25748435
 [11,] -1.25748435
 [12,] -1.25748435
 [13,] -1.25748435
 [14,] -1.25748435
 [15,] -1.25748435
 [16,] -1.25748435
 [17,] -1.25748435
 [18,] -1.25748435
 [19,] -1.25748435
 [20,] -1.25748435
 [21,] -1.25748435
 [22,] -1.25748435
 [23,] -1.25748435
 [24,] -1.25748435
 [25,] -1.25748435
 [26,] -1.25748435
 [27,] -1.25748435
 [28,] -1.25748435
 [29,] -1.25748435
 [30,] -1.25748435
 [31,] -1.25748435
 [32,] -1.25748435
 [33,] -1.25748435
 [34,] -1.25748435
 [35,] -1.25748435
 [36,] -1.25748435
 [37,] -1.25748435
 [38,] -1.25748435
 [39,] -1.25748435
 [40,] -1.25748435
 [41,] -1.25748435
 [42,] -1.25748435
 [43,] -1.25748435
 [44,] -1.25748435
 [45,] -1.25748435
 [46,] -1.25748435
 [47,] -1.25748435
 [48,] -1.25748435
 [49,] -1.25748435
 [50,] -1.25748435
 [51,] -0.03552216
 [52,] -0.03552216
 [53,] -0.03552216
 [54,] -0.03552216
 [55,] -0.03552216
 [56,] -0.03552216
 [57,] -0.03552216
 [58,] -0.03552216
 [59,] -0.03552216
 [60,] -0.03552216
 [61,] -0.03552216
 [62,] -0.03552216
 [63,] -0.03552216
 [64,] -0.03552216
 [65,] -0.03552216
 [66,] -0.03552216
 [67,] -0.03552216
 [68,] -0.03552216
 [69,] -0.03552216
 [70,] -0.03552216
 [71,] -0.03552216
 [72,] -0.03552216
 [73,] -0.03552216
 [74,] -0.03552216
 [75,] -0.03552216
 [76,] -0.03552216
 [77,] -0.03552216
 [78,] -0.03552216
 [79,] -0.03552216
 [80,] -0.03552216
 [81,] -0.03552216
 [82,] -0.03552216
 [83,] -0.03552216
 [84,] -0.03552216
 [85,] -0.03552216
 [86,] -0.03552216
 [87,] -0.03552216
 [88,] -0.03552216
 [89,] -0.03552216
 [90,] -0.03552216
 [91,] -0.03552216
 [92,] -0.03552216
 [93,] -0.03552216
 [94,] -0.03552216
 [95,] -0.03552216
 [96,] -0.03552216
 [97,] -0.03552216
 [98,] -0.03552216
 [99,] -0.03552216
[100,] -0.03552216
[101,]  1.18644003
[102,]  1.18644003
[103,]  1.18644003
[104,]  1.18644003
[105,]  1.18644003
[106,]  1.18644003
[107,]  1.18644003
[108,]  1.18644003
[109,]  1.18644003
[110,]  1.18644003
[111,]  1.18644003
[112,]  1.18644003
[113,]  1.18644003
[114,]  1.18644003
[115,]  1.18644003
[116,]  1.18644003
[117,]  1.18644003
[118,]  1.18644003
[119,]  1.18644003
[120,]  1.18644003
[121,]  1.18644003
[122,]  1.18644003
[123,]  1.18644003
[124,]  1.18644003
[125,]  1.18644003
[126,]  1.18644003
[127,]  1.18644003
[128,]  1.18644003
[129,]  1.18644003
[130,]  1.18644003
[131,]  1.18644003
[132,]  1.18644003
[133,]  1.18644003
[134,]  1.18644003
[135,]  1.18644003
[136,]  1.18644003
[137,]  1.18644003
[138,]  1.18644003
[139,]  1.18644003
[140,]  1.18644003
[141,]  1.18644003
[142,]  1.18644003
[143,]  1.18644003
[144,]  1.18644003
[145,]  1.18644003
[146,]  1.18644003
[147,]  1.18644003
[148,]  1.18644003
[149,]  1.18644003
[150,]  1.18644003
[151,]  1.18644003
[152,]  1.18644003
[153,] -1.25748435
[154,] -1.25748435
[155,] -1.25748435
[156,] -1.25748435
[157,] -1.25748435
[158,] -1.25748435
[159,] -1.25748435
[160,] -1.25748435
[161,] -1.25748435
[162,] -1.25748435
[163,] -1.25748435
[164,] -1.25748435
[165,] -1.25748435
[166,] -1.25748435
[167,] -1.25748435
[168,] -1.25748435
[169,] -1.25748435
[170,] -1.25748435
[171,] -1.25748435
[172,] -1.25748435
[173,] -1.25748435
[174,] -1.25748435
[175,] -1.25748435
[176,] -1.25748435
[177,] -1.25748435
[178,] -1.25748435
[179,] -1.25748435
[180,] -1.25748435
[181,] -1.25748435
[182,] -1.25748435
[183,] -1.25748435
[184,] -1.25748435
[185,] -1.25748435
[186,] -1.25748435
[187,] -0.03552216
[188,] -0.03552216
[189,] -0.03552216
[190,] -0.03552216
[191,] -0.03552216
[192,] -0.03552216
[193,] -0.03552216
[194,] -0.03552216
[195,] -0.03552216
[196,] -0.03552216
[197,] -0.03552216
[198,] -0.03552216
[199,] -0.03552216
[200,] -0.03552216
[201,] -0.03552216
[202,] -0.03552216
[203,] -0.03552216
[204,] -0.03552216
[205,] -0.03552216
[206,] -0.03552216
[207,] -0.03552216
[208,] -0.03552216
[209,] -0.03552216
[210,] -0.03552216
[211,] -0.03552216
[212,] -0.03552216
[213,] -0.03552216
[214,] -0.03552216
[215,] -0.03552216
[216,] -0.03552216
[217,] -0.03552216
[218,] -0.03552216
[219,] -0.03552216
[220,] -0.03552216
[221,] -0.03552216
[222,] -0.03552216
[223,] -0.03552216
[224,] -0.03552216
[225,] -0.03552216
[226,] -0.03552216
[227,] -0.03552216
[228,] -0.03552216
[229,] -0.03552216
[230,] -0.03552216
[231,] -0.03552216
[232,] -0.03552216
[233,]  1.18644003
[234,]  1.18644003
[235,]  1.18644003
[236,]  1.18644003
[237,]  1.18644003
[238,]  1.18644003
[239,]  1.18644003
[240,]  1.18644003
[241,]  1.18644003
[242,]  1.18644003
[243,]  1.18644003
[244,]  1.18644003
[245,]  1.18644003
[246,]  1.18644003
[247,]  1.18644003
[248,]  1.18644003
[249,]  1.18644003
[250,]  1.18644003
[251,]  1.18644003
[252,]  1.18644003
[253,]  1.18644003
[254,]  1.18644003
[255,]  1.18644003
[256,]  1.18644003
[257,]  1.18644003
[258,]  1.18644003
[259,]  1.18644003
[260,]  1.18644003
[261,]  1.18644003
[262,]  1.18644003
[263,]  1.18644003
[264,]  1.18644003
[265,]  1.18644003
[266,]  1.18644003
[267,]  1.18644003
[268,]  1.18644003
[269,]  1.18644003
[270,]  1.18644003
[271,]  1.18644003
[272,]  1.18644003
[273,]  1.18644003
[274,]  1.18644003
[275,]  1.18644003
[276,]  1.18644003
[277,] -1.25748435
[278,] -1.25748435
[279,] -1.25748435
[280,] -1.25748435
[281,] -1.25748435
[282,] -1.25748435
[283,] -1.25748435
[284,] -1.25748435
[285,] -1.25748435
[286,] -1.25748435
[287,] -1.25748435
[288,] -1.25748435
[289,] -1.25748435
[290,] -1.25748435
[291,] -1.25748435
[292,] -1.25748435
[293,] -1.25748435
[294,] -1.25748435
[295,] -1.25748435
[296,] -1.25748435
[297,] -1.25748435
[298,] -1.25748435
[299,] -1.25748435
[300,] -1.25748435
[301,] -1.25748435
[302,] -1.25748435
[303,] -0.03552216
[304,] -0.03552216
[305,] -0.03552216
[306,] -0.03552216
[307,] -0.03552216
[308,] -0.03552216
[309,] -0.03552216
[310,] -0.03552216
[311,] -0.03552216
[312,] -0.03552216
[313,] -0.03552216
[314,] -0.03552216
[315,] -0.03552216
[316,] -0.03552216
[317,] -0.03552216
[318,] -0.03552216
[319,] -0.03552216
[320,] -0.03552216
[321,]  1.18644003
[322,]  1.18644003
[323,]  1.18644003
[324,]  1.18644003
[325,]  1.18644003
[326,]  1.18644003
[327,]  1.18644003
[328,]  1.18644003
[329,]  1.18644003
[330,]  1.18644003
[331,]  1.18644003
[332,]  1.18644003
[333,]  1.18644003
[334,]  1.18644003
[335,]  1.18644003
[336,]  1.18644003
[337,]  1.18644003
[338,]  1.18644003
[339,]  1.18644003
[340,]  1.18644003
[341,]  1.18644003
[342,]  1.18644003
[343,]  1.18644003
[344,]  1.18644003
attr(,"scaled:center")
[1] 2008.029
attr(,"scaled:scale")
[1] 0.8183559
penguins |> 
  map_if(is.numeric, scale) |> 
  as.tibble()
# A tibble: 8 × 5
  species island    bill_length_mm[,1] bill_depth_mm[,1] sex   
  <fct>   <fct>                  <dbl>             <dbl> <fct> 
1 Adelie  Torgersen             -0.883             0.784 male  
2 Adelie  Torgersen             -0.810             0.126 female
3 Adelie  Torgersen             -0.663             0.430 female
4 Adelie  Torgersen             NA                NA     <NA>  
5 Adelie  Torgersen             -1.32              1.09  female
6 Adelie  Torgersen             -0.847             1.75  male  
7 Adelie  Torgersen             -0.920             0.329 female
8 Adelie  Torgersen             -0.865             1.24  male  

pmap()

The map() Family


There are so many functions in the map() family – check out the purrr cheatsheet!

Use functional programming!

https://bookdown.org/hneth/ds4psy

PA 8: The 12 Days of Christmas

https://studioplayhouse.org/the-12-days-of-christmas/

A (boring) Example

How can we print out Timothee Chalamet’s statistics song?

  • We need to repeat “Statistics, yup” many, many times…
map_chr(1:10, ~ "Statistics, yup")
 [1] "Statistics, yup" "Statistics, yup" "Statistics, yup" "Statistics, yup"
 [5] "Statistics, yup" "Statistics, yup" "Statistics, yup" "Statistics, yup"
 [9] "Statistics, yup" "Statistics, yup"
  • …but at different points in the song, he repeats this phrase a different number of times!

Let’s turn this into a function!

chalamet_statistics <- function(n){
  lyrics <- map_chr(1:n, ~ "Statistics, yup")
  
  return(glue("{lyrics}"))
}

The glue package embeds R expressions in curly brackets that are then evaluated and inserted into the argument string.

library(glue)
name <- "Dr. Rehnberg"
glue('My name is {name}.')
My name is Dr. Rehnberg.
chalamet_statistics(n = 8)
Statistics, yup
Statistics, yup
Statistics, yup
Statistics, yup
Statistics, yup
Statistics, yup
Statistics, yup
Statistics, yup

With glue(), long strings get broken by line and concatenated together.

A (better) Example

99 bottles of beer on the wall, 99 bottles of beer. Take one down, pass it around, 98 bottles of beer on the wall…

bottles_lyrics <- function(n){
  lyrics <- glue("{n} bottles of beer on the wall, {n} bottles of beer \nTake one down, pass it around, {n -1} bottles of beer on the wall")
  return(lyrics)
}

bottles_lyrics(3)
3 bottles of beer on the wall, 3 bottles of beer 
Take one down, pass it around, 2 bottles of beer on the wall
bottles_song <- function(n){
  song <- map_chr(n:0, bottles_lyrics)
  return(glue("{song}"))
}

bottles_song(3)
3 bottles of beer on the wall, 3 bottles of beer 
Take one down, pass it around, 2 bottles of beer on the wall
2 bottles of beer on the wall, 2 bottles of beer 
Take one down, pass it around, 1 bottles of beer on the wall
1 bottles of beer on the wall, 1 bottles of beer 
Take one down, pass it around, 0 bottles of beer on the wall
0 bottles of beer on the wall, 0 bottles of beer 
Take one down, pass it around, -1 bottles of beer on the wall

No more bottles of beer on the wall, no more bottles of beer. Go to the store, buy some more, 99 bottles of beer on the wall…

bottles_lyrics <- function(n){
  if(n == 0){
    lyrics <- glue("No more bottles of beer on the wall, no more bottles of beer. \nGo to the store, buy some more, 99 bottles of beer on the wall...")
  } else{
    lyrics <- glue("{n} bottles of beer on the wall, {n} bottles of beer \nTake one down, pass it around, {n -1} bottles of beer on the wall")
  }
  return(lyrics)
}
bottles_song(4)
4 bottles of beer on the wall, 4 bottles of beer 
Take one down, pass it around, 3 bottles of beer on the wall
3 bottles of beer on the wall, 3 bottles of beer 
Take one down, pass it around, 2 bottles of beer on the wall
2 bottles of beer on the wall, 2 bottles of beer 
Take one down, pass it around, 1 bottles of beer on the wall
1 bottles of beer on the wall, 1 bottles of beer 
Take one down, pass it around, 0 bottles of beer on the wall
No more bottles of beer on the wall, no more bottles of beer. 
Go to the store, buy some more, 99 bottles of beer on the wall...

To do…

  • PA 8: The 12 Days of Christmas Starter Functions
    • Due Wednesday 5/24 at 10:00am.
  • Project Proposal + Data
    • Due Monday 5/29 at 11:59pm.

Wednesday, May 24

Today we will…

  • Lab 7 Comments
  • New Material
    • The map2() family
  • Work Time
    • Lab and Challenge 8
    • Project Proposal

Lab 7: Functions + Fish

Get creative with your plots…

  • Rotate your axes (no head tilting!).
  • Use non-default colors.
  • Change font size.
  • Add the legend to your title!
labs(title = str_c("Missing Fish Weights for ",
      "<span style = 'color:#A6CEE3'>**Trip 1**</span>",
      " and <span style = 'color:#1F87B4'>**Trip 2**</span>"),
      subtitle = "by Section of Blackfoot River")

How did I find the color names?

library(RColorBrewer)
brewer.pal(n = 2, name = "Paired")
[1] "#A6CEE3" "#1F78B4" "#B2DF8A"

The map2() Family

These functions allow us to iterate over two lists at the same time.

  • map2()
  • map2_chr()
  • map2_lgl()
  • map2_int()
  • map2_dbl()
  • pmap()

These have two list arguments, denoted x and y.

What is pmap() doing?

Lab + Challenge: 12 Days of Christmas

  1. Write a sing_day() function.
    • What does “one day” lyrics look like?
    • What order do “one day” of lyrics go in?

Tip

  • Start with a small example and test it on a single day outside of the function.
  • glue_collapse() might be useful – find the arguments in the documentation.
  1. Iterate your sing_day() function over a set of days.
  2. Style your output!

To do…

  • Lab 8: The 12 Days of Christmas Full Song
    • Due Friday, 5/26 at 11:59pm.
  • Challenge 8: Styling The 12 Days of Christmas
    • Due Saturday, 5/27 at 11:59pm.
  • Project Proposal + Data
    • Due Monday, 5/29 at 11:59pm.
  • Read Chapter 9: Regression & Simulation
    • Check-in 9.1 & 9.2 due Monday, 5/29 at 10:00am.